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Fungrim entry: 91f156

φ(n)=k=1n{1,gcd ⁣(n,k)=10,otherwise\varphi(n) = \sum_{k=1}^{n} \begin{cases} 1, & \gcd\!\left(n, k\right) = 1\\0, & \text{otherwise}\\ \end{cases}
Assumptions:nZ0n \in \mathbb{Z}_{\ge 0}
TeX:
\varphi(n) = \sum_{k=1}^{n} \begin{cases} 1, & \gcd\!\left(n, k\right) = 1\\0, & \text{otherwise}\\ \end{cases}

n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
Totientφ(n)\varphi(n) Euler totient function
Sumnf(n)\sum_{n} f(n) Sum
GCDgcd ⁣(a,b)\gcd\!\left(a, b\right) Greatest common divisor
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("91f156"),
    Formula(Equal(Totient(n), Sum(Cases(Tuple(1, Equal(GCD(n, k), 1)), Tuple(0, Otherwise)), For(k, 1, n)))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(0))))

Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC